HyperRectangleQuadrature Class

HyperRectangleQuadrature integrates a function over a hypercube.

Inheritance Hierarchy

SystemObject
Imsl.MathHyperRectangleQuadrature

Namespace: Imsl.Math
Assembly: ImslCS (in ImslCS.dll) Version: 6.5.2.0

Syntax

C++

Copy

[SerializableAttribute]
public class HyperRectangleQuadrature

<SerializableAttribute>
Public Class HyperRectangleQuadrature

[SerializableAttribute]
public ref class HyperRectangleQuadrature

[<SerializableAttribute>]
type HyperRectangleQuadrature =  class end

The HyperRectangleQuadrature type exposes the following members.

Constructors

	Name	Description
	HyperRectangleQuadrature(Int32)	Constructs a HyperRectangleQuadrature object.
	HyperRectangleQuadrature(IRandomSequence)	Constructs a HyperRectangleQuadrature object.

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Methods

	Name	Description
	Equals	Determines whether the specified object is equal to the current object. (Inherited from Object.)
	Eval(HyperRectangleQuadratureIFunction)	Returns the value of the integral over the unit cube.
	Eval(HyperRectangleQuadratureIFunction, Double, Double)	Returns the value of the integral over a cube.
	Finalize	Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection. (Inherited from Object.)
	GetHashCode	Serves as a hash function for a particular type. (Inherited from Object.)
	GetType	Gets the Type of the current instance. (Inherited from Object.)
	MemberwiseClone	Creates a shallow copy of the current Object. (Inherited from Object.)
	ToString	Returns a string that represents the current object. (Inherited from Object.)

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Properties

	Name	Description
	AbsoluteError	Sets the absolute error tolerance.
	ErrorEstimate	Returns an estimate of the relative error in the computed result.
	NumberOfProcessors	Perform the parallel calculations with the maximum possible number of processors set to NumberOfProcessors.
	Parallel	Enable or disable performing HyperRectangleQuadrature.IFunction.F in parallel.
	RelativeError	Sets the relative error tolerance.

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Remarks

This class is used to evaluate integrals of the form:

$\int_{a_{n-1}}^{b_{n-1}} \cdots \int_{a_0}^{b_0} f(x_0,\ldots,x_{n-1}) \, dx_0 \ldots dx_{n-1}$

Integration of functions over hypercubes by Monte Carlo, in which the integral is evaluated as the value of the function averaged over a sequence of randomly chosen points. Under mild assumptions on the function, this method will converge like $1 / \sqrt{n}$ , where n is the number of points at which the function is evaluated.

It is possible to improve on the performance of Monte Carlo by carefully choosing the points at which the function is to be evaluated. Randomly distributed points tend to be non-uniformly distributed. The alternative to a sequence of random points is a low-discrepancy sequence. A low-discrepancy sequence is one that is highly uniform.

This function is based on the low-discrepancy Faure sequence as computed by FaureSequence.

Reference

Imsl.Math Namespace

Other Resources

Example